Solution Found!
If Y has a geometric distribution with probability of
Chapter 3, Problem 147E(choose chapter or problem)
If has a geometric distribution with probability of success
, show that the moment-generating function for
is
\(m(t)=\frac{p e^{t}}{1-q e^{t}}\), where \(q=1-p\).
Equation Transcription:
Text Transcription:
m(t)=pe^t over 1-qe^t
q=1-p
Questions & Answers
QUESTION:
If has a geometric distribution with probability of success
, show that the moment-generating function for
is
\(m(t)=\frac{p e^{t}}{1-q e^{t}}\), where \(q=1-p\).
Equation Transcription:
Text Transcription:
m(t)=pe^t over 1-qe^t
q=1-p
ANSWER:
Solution 147E
Step1 of 2:
We have a random variable ‘Y’ and it follows geometric distribution with parameter ‘p’.
Then the probability mass function of geometric distribution is given by:
Where,
x = random variable
p = probability of success(Parameter)
n = sample size
We need to show that the moment generating function for Y is , where q = 1- p.
Step2 of 2:
Consider,